微积分代写 SECTION:DIRECTIONS: Show all the work in the space provided. Please box final answers, andfollow the indicated directions.1.Find the domain ···
PRACTICE TEST 微积分代写
DIRECTIONS: Show all the work in the space provided. Please box final answers, and
follow the indicated directions.
1.Find the domain and the range of the function
2.Use linear approximation (differentials) of the function
then use a calculator to find the percentage error.
a) Is f continuous at (1,3)? Justify your answer.
b) Is f continuous at (0,0)? Justify your answer.微积分代写
4.a) Given the function f (x, y,z) = x2 y + x 1+ z find the directional derivative at the point (x, y,z) = (1,2,3), in the direction of
b) Find the direction of the greatest slope at the given point.
c) Find the magnitude of the greatest slope at the given point
6.a) Find the critical points of the function f (x, y) = 3xy − x2 y − xy 2 .
b) Classify these points as local maxima, minima, or saddle points
7.Find the maximum value of the function f (x, y) = 4xy 2 − x 2 y 2 − xy 3 on the domain D which is the closed triangular region with vertices (0,0), (6,0) and (0,6).